4 ms·
Not the GP, but you have to take into account that these are studies done by mathematicians, not physicists, so there are to points to consider. First, weakeni
by gjulian 9y ago
Not the GP, but you have to take into account that these are studies done by mathematicians, not physicists, so there are to points to consider.
First, weakening is not related to uncertainty, at least not in the normal sense that I think you refer to. It is not related to the physical solution itself but to our own rules of what we consider a solution. If instead of vector fields we were working with animals, the strong solution would be "we need this animal to be a duck" and the weakened one is "we need this animal to quack when we poke it with a stick". So it is not similar to the quantum uncertainty principle nor anything like it.
Second, mathematicians are interested only in these specific equations. Breaking the equations means that they do not model correctly the real world, and finding those new equations is the job of physicists. Maybe there are other conditions on the solutions, or maybe the relaxation they did allows for non-physical solutions. In fact, they do not prove that those solutions satisfy the energy inequality, so it might be possible that all but one of those non-unique solutions are only possible if you allow fluids to magically gain energy out of nowhere (which obviously conflicts with thermodynamic laws).
- im3w1l 9y agoReminds me of the Banach-Tarski paradox, where non-smoothness breaks conservation.
- snakeboy 9y agoCan you elaborate on what you mean here? Isn't B-T just a consequence of accepting the axiom of choice and performing some pathological decompositions of a ball? What do you mean by: >non-smoothness breaks conservation
- im3w1l 9y agoNormally translations and rotations conserve volume. But not when you have these extremely non-smooth pieces.
- claudius 9y ago> Breaking the equations means that they do not model correctly the real world This is wrong. We already know that these equations do not model correctly the real world. No model correctly models the real world and every model breaks down eventually at one point or another. Showing that a certain set of equations leads to non-unique results under certain conditions means nothing, unless you also show that those ‘certain conditions’ are true in cases where we previously assumed the model to hold. If you only show that in cases where we previously also assumed the equations not to hold, they actually output nonsense, this may be a mathematically curious and nice result but of no physical relevance. So far, this result looks more like realising that Newton’s gravitational field diverges for a point particle of nonzero mass, which is not really any indication whatsoever that it doesn’t correctly model the real world.